Heretofore, it has been well known to provide an orthodontic appliance in the form of a tooth positioner having a molded arch-shaped body of resilient material with sockets for engagement with the teeth of one or both arches of a person. It has also been well known to mold rigid means into the body of the positioner for enhancing positioning and orientation of the appliance and in some respects to control rotation as shown in U.S. Pat. No. 3,510,946. The rigid elements shown in this patent are designed to fit directly over one or more selected teeth, and more particularly to fit over a portion or all of a tooth. However, the elements are independent of one another and rely strictly upon the relationship between the appliance body and the element to which it is formed.